A263209 Decimal expansion of the imaginary part of the continued fraction i/(e + i/(e + i/(...))).

3, 5, 5, 8, 8, 1, 7, 2, 7, 1, 0, 7, 5, 6, 2, 7, 8, 2, 6, 3, 1, 3, 1, 9, 4, 9, 8, 1, 3, 7, 5, 2, 9, 7, 4, 3, 4, 6, 8, 7, 2, 7, 9, 2, 7, 5, 7, 6, 6, 4, 8, 1, 1, 6, 6, 4, 5, 3, 2, 5, 3, 6, 8, 6, 8, 8, 7, 6, 3, 2, 1, 5, 4, 6, 7, 7, 0, 0, 3, 7, 4, 3, 8, 1, 2, 3, 7, 0, 9, 5, 6, 9, 8, 7, 6, 7, 1, 2, 7, 5, 9, 9, 3, 3, 4

Offset

0,1

Comments

Here, i is the imaginary unit sqrt(-1) and e is the Euler number.

For the real part of this constant, and for more comments, see A263208.

Links

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Formula

Equals the imaginary part of (sqrt(e^2 + 4 * i) - e)/2.

Example

0.355881727107562782631319498137529743468727927576648116645325368688...

Maple

evalf((16 + exp(4))^(1/4) * sin(arctan(4/exp(2))/2) / 2, 120); # Vaclav Kotesovec, Nov 06 2015

Mathematica

RealDigits[Im[(Sqrt[E^2 + 4I] - E)/2], 10, 100][[1]] (* Alonso del Arte, Oct 12 2015 *)

Prog

(PARI) imag((-exp(1)+sqrt(exp(2)+4*I))/2)

Crossrefs

Cf. A001113, A263208.

Sequence in context: A019632 A021285 A138575 * A101330 A063285 A316938

Adjacent sequences: A263206 A263207 A263208 * A263210 A263211 A263212

Keyword

nonn,cons

Author

Stanislav Sykora, Oct 12 2015

Status

approved